P. Nalbach — Page 2

arXiv1998

Rotating wave approximation: systematic expansion and application to coupled spin pairs

We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments.

cond-mat.dis-nn↗

arXiv1997

Cubic Defects: Comparing the Eight-State-System with its Two-Level-Approximation

Substitutional defects in a cubic symmetry (such as a lithium defect in a KCl host crystal) can be modeled appropriately by an eight-state-system. Usually this tunneling degree of freedom is approximated by a two-level-system. We investigate the observable differences between the two models in three contexts. First we show that the two models predict different relations between the temperature dependence of specific heat and static susceptibility. Second we demonstrate that in the presence of external forces (pressure and electric field) the eight-state-system shows features that cannot be understood within the framework of the two-level-approximation. In this context we propose an experiment for measuring the parameter for tunneling along the face diagonal. Finally we discuss the differences between the models appearing for strongly coupled pairs. Geometric selection rules and particular forms of asymmetry lead to clear differences between the two models.

cond-mat.dis-nn↗